Rewrite as a simplified fraction. ${3.8\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 382.2222...\\ 10x &= 38.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 344}$ ${x = \dfrac{344}{90}} $ ${x = \dfrac{172}{45}} \text{or} {3 \dfrac{37}{45}}$